Results 21 to 30 of about 8,745 (203)

Spatiotemporal dynamics and Turing patterns in an eco-epidemiological model with cannibalism

Results in Control and Optimization, 2022
In this work, we have studied the spatiotemporal dynamics and pattern formation in an eco-epidemiological model with cannibalism, which are not explored in the existing literature.
Vikas Kumar, Nitu Kumari, Ravi P. Agarwal   +2 more
doaj   +1 more source

Bifurcation Analysis of a Generic Reaction–Diffusion Turing Model [PDF]

International Journal of Bifurcation and Chaos, 2014
A generic Turing type reaction–diffusion system derived from the Taylor expansion near a constant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations is obtained. The bifurcation direction and the stability of the bifurcating periodic obits are calculated.
Liu, Ping, Shi, Junping, Wang, Rui, Wang, Yuwen   +3 more
openaire   +1 more source

Additive Global Noise Delays Turing Bifurcations

Physical Review Letters, 2007
We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order,
Hutt, Axel, Longtin, Andre, Schimansky-Geier, Lutz   +2 more
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Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns

Scientific Reports, 2021
The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation.
Shan Guo, Ming-zhu Sun, Xin Zhao
doaj   +1 more source

Cross-diffusion-driven Turing instability and weakly nonlinear analysis of Turing patterns in a uni-directional consumer-resource system

Boundary Value Problems, 2017
Spatiotemporal patterns driven by cross-diffusion of a uni-directional consumer-resource (C-R) system with Holling-II type functional response are investigated in this paper.
Renji Han, Binxiang Dai
doaj   +1 more source

Turing-Hopf patterns in a morphochemical model for electrodeposition with cross-diffusion

Applications in Engineering Science, 2021
This paper focuses on the impact of cross-diffusion for Turing-Hopf instability in a morphochemical model for electrodeposition (DIB) and completes the analysis on the role of cross-diffusion on pattern formation in electrodeposition we recently carried ...
Deborah Lacitignola, Ivonne Sgura, Benedetto Bozzini   +2 more
doaj   +1 more source

Coupled Effects of Turing and Neimark-Sacker Bifurcations on Vegetation Pattern Self-Organization in a Discrete Vegetation-Sand Model

Entropy, 2017
Wind-induced vegetation patterns were proposed a long time ago but only recently a dynamic vegetation-sand relationship has been established. In this research, we transformed the continuous vegetation-sand model into a discrete model.
Feifan Zhang, Huayong Zhang, Tousheng Huang, Tianxiang Meng, Shengnan Ma   +4 more
doaj   +1 more source

A graph-theoretic method for detecting potential Turing bifurcations [PDF]

The Journal of Chemical Physics, 2006
The conditions for diffusion-driven (Turing) instabilities in systems with two reactive species are well known. General methods for detecting potential Turing bifurcations in larger reaction schemes are, on the other hand, not well developed. We prove a theorem for a graph-theoretic condition originally given by Volpert and Ivanova [Mathematical ...
Mincheva, Maya, Roussel, Marc R.
openaire   +2 more sources

Boundary Conditions Cause Different Generic Bifurcation Structures in Turing Systems [PDF]

Bulletin of Mathematical Biology, 2022
AbstractTuring’s theory of morphogenesis is a generic mechanism to produce spatial patterning from near homogeneity. Although widely studied, we are still able to generate new results by returning to common dogmas. One such widely reported belief is that the Turing bifurcation occurs through a pitchfork bifurcation, which is true under zero-flux ...
openaire   +3 more sources

Bifurcation, Chaos, and Pattern Formation for the Discrete Predator-Prey Reaction-Diffusion Model

Discrete Dynamics in Nature and Society, 2019
In this paper, a discrete predator-prey system with the periodic boundary conditions will be considered. First, we get the conditions for producing Turing instability of the discrete predator-prey system according to the linear stability analysis.
Lili Meng, Yutao Han, Zhiyi Lu, Guang Zhang   +3 more
doaj   +1 more source